Vibration of double-walled carbon nanotubes coupled by temperature-dependent medium under a moving nanoparticle with multi physical fields

A numerical model on nonlinear vibration of double-walled carbon nanotubes (DWCNTs) subjected to a moving nanoparticle and multi physical fields is proposed. DWCNTs are considered with the kinematic assumption of Euler–Bernoulli beam theory. The surrounding elastic substrate is simulated as Pasternak foundation, which is assumed to be temperature-dependent. Hamilton's principle, incremental harmonic balanced method, Galerkin, and time integration method with direct iteration are employed to establish the equations of motion of zigzag DWCNTs. The study reveals that for the weak van der Waals forces, DWCNTs have the positive and the negative deflections as if it vibrates under a moving nanoparticle.